Observing gravitational-wave transient GW150914with minimal assumptions

B. P. Abbott et al.*

(LIGO Scientific Collaboration and Virgo Collaboration)(Received 25 February 2016; published 7 June 2016)

The gravitational-wave signal GW150914 was first identified on September 14, 2015, by searches forshort-duration gravitational-wave transients. These searches identify time-correlated transients in multipledetectors with minimal assumptions about the signal morphology, allowing them to be sensitive togravitational waves emitted by a wide range of sources including binary black hole mergers. Over theobservational period from September 12 to October 20, 2015, these transient searches were sensitive tobinary black hole mergers similar to GW150914 to an average distance of ∼600 Mpc. In this paper, wedescribe the analyses that first detected GW150914 as well as the parameter estimation and waveformreconstruction techniques that initially identified GW150914 as the merger of two black holes. We find thatthe reconstructed waveform is consistent with the signal from a binary black hole merger with a chirp massof ∼30 M⊙ and a total mass before merger of ∼70 M⊙ in the detector frame.

DOI: 10.1103/PhysRevD.93.122004

I. INTRODUCTION

The newly upgraded Advanced LIGO observatories[1,2], with sites near Hanford, Washington (H1), andLivingston, Louisiana (L1), host the most sensitivegravitational-wave detectors ever built. The observatoriesuse kilometer-scale Michelson interferometers that aredesigned to detect small, traveling perturbations inspace-time predicted by Einstein [3,4], and thought toradiate from a variety of astrophysical processes. AdvancedLIGO recently completed its first observing period, fromSeptember 2015 to January 2016. Advanced LIGO isamong a generation of planned instruments that includesGEO 600, Advanced Virgo, and KAGRA; the capabilitiesof this global gravitational-wave network should quicklygrow over the next few years [5–8].An important class of sources for gravitational-wave

detectors are short duration transients, known collectivelyas gravitational-wave bursts [9]. To search broadly for awide range of astrophysical phenomena, we employunmodeled searches for gravitational-wave bursts of dura-tions ∼10−3−10 s, with minimal assumptions about theexpected signal waveform. Bursts may originate from arange of astrophysical sources, including core-collapsesupernovae of massive stars [10] and cosmic string cusps[11]. An important source of gravitational-wave transientsare the mergers of binary black holes (BBH) [12–14]. Burstsearches in data from the initial generation of interferom-eter detectors were sensitive to distant BBH signals frommergers with total masses in the range ∼20–400 M⊙[15,16]. Since burst methods do not require precise

waveform models, the unmodeled search space mayinclude BBH mergers with misaligned spins, large massratios, or eccentric orbits. A number of all-sky, all-timeburst searches have been performed on data from initialLIGO and Virgo [17–19]. Recent work has focussed onimproving detection confidence in unmodeled searches,and the last year has seen several improvements in theability to distinguish astrophysical signals from noisetransients [20–24]. As a result, burst searches are nowable to make high confidence detections across a wideparameter space.On September 14, 2015, an online burst search [25]

reported a transient that clearly stood above the expectedbackground from detector noise [26]. The alert came only3 min after the event’s time stamp of 09∶50∶45UTC. Asecond online burst search independently identified theevent with a latency of a few hours, providing a rapidconfirmation of the signal [23]. The initial waveformreconstruction showed a frequency evolution that rises intime, suggesting binary coalescence as the likely progen-itor, and a best fit model provided a chirp mass around28M⊙, indicating the presence of a BBH signal. Withindays of the event, many follow-up investigations began,including detailed checks of the observatory state to checkfor any possible anomalies [27]. Two days after the signalwas found, a notice with the estimated source position wassent to a consortium of astronomers to search for possiblecounterparts [28]. Investigations continued over the nextseveral months to validate the observation, estimate itsstatistical significance, and characterize the astrophysicalsource [29,30].In this article, we present details of the burst searches that

made the first detection of the gravitational-wave transient,*Full author list given at the end of the article.

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GW150914, announced in [26]. We describe resultsreported in this announcement that are based on thecoherent Waveburst algorithm, along with those obtainedby two other analyses using omicron-LALInference-Burstsand BayesWave [23,25,31]. In Sec. II, we present a briefoverview of the quality of the acquired data and detectorperformance, before moving on, in Sec. III, to present thethree analyses employed. Using each pipeline, we assessthe statistical significance of the event. Section IV char-acterizes each search sensitivity using simulated signalsfrom BBH mergers. In Sec. V, we demonstrate how a rangeof source properties may be estimated using these sametools—including sky position and masses of the blackholes. The reconstructed signal waveform is directlycompared to results from numerical relativity (NR) simu-lations, giving further evidence that this signal is consistentwith expectations from general relativity. Finally, the paperconcludes with a discussion about the implications ofthis work.

II. DATA QUALITY ANDBACKGROUND ESTIMATION

We identify 39 calendar days of Advanced LIGO data,from September 12 to October 20, 2015, as a data set tomeasure the sensitivity of the searches and the impact ofbackground noise events, known as glitches.As in previous LIGO, Virgo and GEO transient searches

[17–19], a range of monitors tracking environmental noiseand the state of the instruments are used to discard periodsof poor quality data. Numerous studies have been per-formed to identify efficient veto criteria to remove non-Gaussian noise features, while having the smallest possibleimpact on detector live time [27].However, it is not possible to remove all noise glitches

based on monitors. This leaves a background residual thathas to be estimated from the data. To calculate the back-ground rate of noise events arising from glitches occurringsimultaneously at the two LIGO sites by chance [17–19],the analyses are repeated on Oð106Þ independent time-shifted data sets. Those data sets are generated by trans-lating the time of data in one interferometer by a delay ofsome integer number of seconds, much larger than themaximum GW travel time≃10 ms between the Livingstonand Hanford facilities. By considering the whole coincidentlive time resulting from each artificial time shift, we obtainthousands of years of effective background based on theavailable data. With this approach, we estimate a falsealarm rate (FAR) expected from background for eachpipeline.The “time-shift” method is effective to estimate the

background due to uncorrelated noise sources at the twoLIGO sites. For the time immediately around GW150914,we also examined potential sources of correlated noisebetween the detectors, and concluded that all possible

sources were too weak to have produced the observedsignal [27].

III. SEARCHES FORGRAVITATIONAL-WAVE BURSTS

Strain data are searched by gravitational-wave burstsearch algorithms without assuming any particular signalmorphology, origin, direction or time. Burst searches areperformed in two operational modes: online and off-line.Online, low-latency searches provide alerts within

minutes of a GW signal passing the detectors to facilitatefollow-up analyses such as searching for electromagneticcounterparts. In the days and weeks following the datacollection, burst analyses are refined using updated infor-mation on the data quality and detector calibration toperform off-line searches. These off-line searches provideimproved detection confidence estimates for GW candi-dates, measure search sensitivity, and add to waveformreconstruction and astrophysical interpretation. For short-duration, narrowband signals, coherent burst searcheshave sensitivities approaching those of optimal matchedfilters [16,32].In the following subsections, we describe the burst

analysis of GW150914. This includes two independentend-to-end pipelines, coherent Waveburst (cWB) andomicron-LALInference-Bursts (oLIB), and BayesWave,which performed a follow-up analysis at trigger timesidentified by cWB. These three algorithms employ differentstrategies (and implementations) to search for unmodeledGW transients; hence, they could perform quite differentlyfor specific classes of GW signals. Given the very broadcharacter of burst signals, the use of multiple searchalgorithms is then beneficial, both to validate results andto improve coverage of the wide signal parameter space.A summary of the results from cWB has been presented

in [26]. Here, we provide more details regarding the cWBsearch pertaining the discovery of GW150914 and presentits results with respect to the other burst searches. In thispaper, we focus our characterizations of our pipelines onBBH sources only.

A. Coherent WaveBurst

The cWB algorithm has been used to perform all-skysearches for gravitational-wave transients in LIGO, Virgoand GEO data since 2004. The most recent cWB resultsfrom the initial detectors are [17,19,33]. The cWB algo-rithm has since been upgraded to conduct transient searcheswith the advanced detectors [24]. The cWB pipeline wasused in the low-latency transient search that initiallydetected GW150914, reporting the event 3 min after thedata were collected. This search aims at rapid alerts for theLIGO/Virgo electromagnetic follow-up program [28] andprovides a first estimation of the event parameters and skylocation. A slightly different configuration of the same

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pipeline was used in the off-line search to measure thestatistical significance of the GW150914 event, which wasreported in [26]. The low-latency search was performed inthe frequency range of 16–2048 Hz, while the off-linesearch covered the band of the best detector sensitivitybetween 16 and 1024 Hz.

1. cWB pipeline overview

The cWB pipeline searches for a broad range ofgravitational-wave transients in the LIGO frequency bandwithout prior knowledge of the signal waveforms [25]. Thepipeline identifies coincident events in data from the twoLIGO detectors and reconstructs the gravitational-wavesignal associated with these events using a likelihoodanalysis.First, the data are whitened and converted to the time-

frequency domain using the Wilson-Daubechies-Meyerwavelet transform [34]. Data from both detectors are thencombined to obtain a time-frequency power map. A transientevent is identified as a cluster of time-frequency data sampleswith power above the baseline detector noise. To obtain agood time-frequency coverage for a broad range of signalmorphologies, the analysis is repeated with seven frequencyresolutionsΔf ranging from 1 to 64 Hz in steps of powers of2, corresponding to time resolutions Δt ¼ 1=ð2ΔfÞ from500 to 7.8 ms. The clusters at different resolutions over-lapping in time and frequency are combined into a triggerthat provides a multiresolution representation of the excesspower event recorded by the detectors.The data associated with each trigger are analyzed

coherently [24] to estimate the signal waveforms, the wavepolarization, and the source sky location. The signal wave-forms in both detectors are reconstructed with the con-strained likelihood method [35]. The constraint used in thisanalysis is model independent and requires the reconstructedwaveforms to be similar in both detectors, as expected fromthe close alignment of the H1 and L1 detector arms.The waveforms are reconstructed over a uniform grid of

sky locations with 0.4° × 0.4° resolution. We select the bestfit waveforms that correspond to the maximum of thelikelihood statistic L ¼ ccEs, where Es is the total energyof the reconstructed waveforms1 and cc measures thesimilarity of the waveforms in the two detectors. Thecoefficient cc is defined as cc ¼ Ec=ðEc þ EnÞ, where Ec isthe normalized coherent energy and En is the normalizedenergy of the residual noise after the reconstructed signal issubtracted from the data. The coherent energy Ec isproportional to the cross-correlation between the recon-structed signal waveforms in H1 and L1 detectors.Typically, gravitational-wave signals are coherent and havesmall residual energy, i.e., Ec ≫ En and therefore cc ∼ 1.On the other hand, spurious noise events (glitches) are oftennot coherent, and have large residual energy because the

reconstructed waveforms do not fit the data well, i.e., Ec ≪En and therefore cc ≪ 1. The ranking statistic is defined asηc ¼ ð2ccEcÞ1=2. By construction, it favors gravitational-wave signals correlated in both detectors and suppressesuncorrelated glitches.

2. Classification of cWB events

Events produced by the cWB pipeline with cc > 0.7 areselected and divided into three search classes C1, C2, andC3 according to their time-frequency morphology. Thepurpose of this event classification is to account forthe non-Gaussian noise that occurs nonuniformly acrossthe parameter space searched by the pipeline.The classes are determined by three algorithmic tests

and additional selection cuts. The first algorithmic testaddresses a specific type of noise transient referred to as“blip glitches” [27]. During the run, both detectors expe-rienced noise transients of unknown origin consisting of afew cycles around 100 Hz. These blip glitches have a verycharacteristic time-symmetric waveform with no clearfrequency evolution. Previous work has shown thatdown-weighting signals with simple time-frequency struc-ture can enhance pipeline performance [21]. To implementthis here, we apply a test that uses waveform properties toidentify, in the time domain, blip glitches occurring at bothdetectors. The second algorithmic test identifies glitchesdue to nonstationary narrow-band features, such as powerand mechanical resonance lines. This test selects candidateswhich have most of their energy (greater than 80%)localized in a frequency bandwidth less than 5 Hz. AcWB event is placed in the search class C1, if it passeseither of the aforementioned tests. In addition, due to theelevated nonstationary noise around and below theAdvanced LIGO mechanical resonances at 41 Hz, eventswith central frequency lower than 48 Hz were also placedin the C1 class.The third algorithmic test is used to identify events with a

frequency increasing with time. The reconstructed time-frequency patterns can be characterized by an ad hocparameterM following Eq. (1) in Sec. V D. For coalescingbinary signals M corresponds to the chirp mass of thebinary [36]. For signals that do not originate from coa-lescing binaries and glitches, M takes on unphysicalvalues. In the unmodeled cWB analysis, the parameterM is used to distinguish between events with differenttime-frequency evolution. By selecting events withM > 1M⊙ we identify a broad class of events with achirping time-frequency signature, which includes a sub-class of coalescing binary signals. The events selected bythis test that also have a residual energy En consistent withGaussian noise are placed in the search class C3. All otherevents, not included in the C1 or C3 class, are placed in thesearch class C2. The union of all three independent searchclasses covers the full parameter space accessible to theunmodeled cWB search.1 ffiffiffiffiffi

Esp

is the network signal-to-noise ratio [24].

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3. False alarm rate

To establish the distribution of background events, weuse the time-shift procedure discussed in Sec. II, using allthe data available for each detector. The effective back-ground live time for this analysis is 67 400 years, obtainedby analyzing more than 1.6 × 106 time-shifted instancesof 16 days of the observation time. Figure 1 reports thecumulative false alarm rate distributions as a function of thedetection statistic ηc for the three defined search classes.The significance of a candidate event is measured againstthe background of its class. As shown in the plot, theC1 search class is affected by a tail of blip glitches withthe false alarm rate of approximately 0.01y−1. Confiningglitches in the C1 class enhances the search sensitivity togravitational-wave signals falling in the C2 and C3classes. In fact, the tail is reduced by more than twoorders of magnitude in the C2 search class. The

background rates in the C3 search class are almost tentimes lower than in C2, with no prominent tail of loudevents, indicating that it is highly unlikely for detectors toproduce coherent background events with a chirpingtime-frequency evolution.To check the homogeneity and stability of background

rates shown in Fig. 1, these distributions have beencompared between instances of background data, generatedwith different time shifts between the detectors, finding noevidence for any dependence on the time-shift interval oron the time period of data collection.

4. Significance of GW150914 event

GW150914 was detected with ηc ¼ 20 and belongsto the C3 class. Its ηc value is larger than the detectionstatistic of all observed cWB candidates. Also Fig. 2 (left)shows that the GW150914 ηc value is larger than thedetection statistic of any background event in its searchclass in 67 400 years of the equivalent observation time.All other observed event candidates (orange squares) areconsistent with the background.The GW150914 significance is defined by its false

alarm rate measured against the background in the C3class. Assuming that all search classes are statisticallyindependent, this false alarm rate should be increased by aconservative trials factor equal to the number of classes.By taking into account the trials factor of 3, the estimatedGW150914 false alarm rate is less than one event in22 500 years. The probability that the 16 days of datawould yield a noise event with this false alarm rate is lessthan 16=ð365 × 22 500Þ ¼ 2 × 10−6.The union of the C2 and C3 search classes represents a

transient search with no assumptions on the signal time-frequency evolution. The result of such analysis with justtwo search classes C1 and C2þ C3 is shown in Fig. 2

FIG. 1. Cumulative rate distribution of background events as afunction of the detection statistic ηc for the three cWB searchclasses. Vertical dashed line shows the value of the detectionstatistic for the GW150914 event.

FIG. 2. Search results (in orange) and expected number of background events (black) in 16 days of the observation time as a functionof the cWB detection statistic (bin size 0.2) for the C3 search class (left) and C2þ C3 search class (right). The black curve shows thetotal number of background events found in 67 400 years of data, rescaled to 16 days of observation time. The orange star representsGW150914, found in the C3 search class.

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(right). In this case there are four events louder thanGW150914 in the C2þ C3 class. With the trials factorof 2, the false alarm rate is one event in 8 400 years. Thefour loud events are produced by a random coincidenceof multiple blip glitches: two nearby blip glitches in onedetector and a single blip glitch in the second detector.The algorithmic test that identifies blip glitches was notdesigned to capture multiple ones and, therefore, missedthese events.

B. oLIB

The oLIB search [23] is a search pipeline forgravitational-wave bursts designed to operate in lowlatency, with results typically produced in around30 min. However, the pipeline can operate in two modes,online and off-line. The online version identifiedGW150914 independently of cWB. The off-line versionis used here to establish the significance of GW150914.

1. oLIB pipeline overview

The oLIB pipeline follows a hierarchical scheme, firstperforming a coincident event down selection followedby a fully coherent Markov chain Monte Carlo Bayesiananalysis.In the first step of the pipeline, a time-frequency map of

the single-interferometer strain data from all detectors isproduced using the Q-transform [37] implemented inOmicron [38]. Stretches of excess power are flagged astriggers. Neighboring triggers that occur within 100 ms,with an identical central frequency f0 and quality factor Q,are clustered together. After applying data quality vetoes asdescribed in Sec. II, a list of triggers that fall within a 10 mscoincidence window (compatible with the speed-of-lightbaseline separation of the detectors) is then compiled.In the second step of the pipeline, all coincident triggers

identified in the first step are analyzed using LIB, aBayesian parameter estimation and model selection algo-rithm that coherently explores the signal parameter spacewith the nested sampling algorithm [39] available in theLALInference software library [40].LIB models signals and glitches by a single sine-

Gaussian wavelet. Signals have a coherent phase acrossdetectors, while glitches do not. Using this model, LIBcalculates two Bayes factors, each of which represents anevidence ratio between two hypotheses: coherent signal vsGaussian noise (BSN) and coherent signal vs incoherentglitch (BCI). These two Bayes factors are then combinedinto a scalar likelihood ratio Λ for the signal vs noise(Gaussian or glitch) problem. More precisely, Λ is obtainedfrom the ratio of the probability distributions for the Bayesfactors BSN and BCI estimated empirically from “training”sets of events. Those sets consists of ≃4000 simulatedgravitational-wave signals from a uniform-in-volumesource distribution and≃150 background triggers obtained

from time-shifted data for the signal and noise cases,respectively.The final ranking statistic Λ is evaluated for a different

set of background triggers from time-shifted data in order tomap a given value of the likelihood ratio into a FAR.

2. oLIB analysis of GW150914

For the purpose of this analysis, Omicron runs over the32–1024 Hz bandwidth and selects triggers that exceed aSNR threshold of 6.5. LIB uses the following priors:uniform in sky location, uniform in central frequencyf0 in the selected bandwidth, and uniform in quality factorQ from 0.1–110. Events with BSN or BCI ≤ 0 arediscarded. We retain events with 48 ≤ ~f0 ≤ 1020 Hz and2 ≤ ~Q ≤ 109, where ~f0 and ~Q are median values computedfrom the posterior distributions delivered by LIB. Theselection cut on ~Q is analogous to those used by cWB toreject blip glitches and narrow-band features. The rankingstatistic Λ and its background distribution from whichthe FAR is deduced are computed from the training andbackground sets after applying all those cuts.Because oLIB is able to run on short data segments

(≳3 s), this search analyzed nearly all available data, whichamounted to 17.4 days, i.e., ∼10% more coincident datathan cWB. The data were time-shifted in 1-sec intervals toproduce the equivalent of 106 000 years of backgrounddata. The background distribution is plotted as a function oflogΛ in Fig. 3. As shown in the same figure GW150914has a ranking statistic of logΛ ¼ 0.80, corresponding to aFAR of roughly 1 in 27 000 years. It is the only event in thesearch results satisfying the selection cuts.

C. BayesWave follow-up

The BayesWave pipeline is a Bayesian algorithmdesigned to robustly distinguish GW signals from glitchesin the detectors [31,41]. In this search, BayesWave is run as

FIG. 3. Cumulative rate distribution of background events as afunction of oLIB ranking statistic logΛ. GW150914 is the onlyevent in the search results to pass all thresholds. Its statisticvalue logΛ ¼ 0.80 corresponds to a background FAR of ≃1 in27 000 years.

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a follow-up analysis to triggers identified by cWB. For eachcandidate event, BayesWave compares the marginalizedlikelihood, or evidence, among three hypotheses: the datacontain only Gaussian noise, the data contain Gaussiannoise and noise transients (glitches), or the data containGaussian noise and an astrophysical signal.The BayesWave algorithm models signals and glitches

using a linear combination of sine-Gaussian wavelets.The number of wavelets needed in the glitch or signalmodel is not fixed a priori, but instead is optimized using areversible jump Markov chain Monte Carlo. The glitchmodel fits the data separately in each interferometer with anindependent linear combination of wavelets. The signalmodel reconstructs the candidate event at some fiduciallocation (the center of the Earth), taking into account theresponse of each detector in the network to that signal.BayesWave uses a parametrized phenomenological model,BayesLine, for the instrument noise spectrum, simultane-ously characterizing the Gaussian noise and instrument/astrophysical transients [41].BayesWave produces posterior distributions for the

parameters of each model under consideration. For thesignal model, this includes the waveform, as constructedfrom sums of sine-Gaussian wavelets, and the sourceposition. Waveform reconstructions are used to produceposterior distributions for characteristics such as theduration, central frequency, and bandwidth of the signal,which are used to compare the data to theoretical models.The marginalized posterior (evidence) for each model iscalculated by marginalizing over the different dimensionwaveform reconstructions, and then is used to rank thecompeting hypotheses.BayesWave is used as a follow-up analysis for candidate

events first identified by cWB. The combined cWBþBayesWave data analysis pipeline has been shown to allowhigh-confidence detections across a range of waveformmorphologies [21,22]. The cWBþ BayesWave pipelineuses the Bayes factor, comparing the signal and glitchmodels (BSG) as its detection statistic. Bayes factors arereported on a natural logarithmic scale lnBSG, whichscales with N ln SNR, where N is the number of waveletsused in the reconstruction [22]. The consequence is thatBayesWave assigns a higher detection statistic to signalswith nontrivial time-frequency structure. Though Bayesfactors used by Bayeswave and oLIB methods bothproduce a measure of coherence between the signalmorphologies observed in multiple detectors, the abovecalculation indicates that BayesWave, BSG, also includes ameasure of the signal complexity.The “off-line” BayesWave pipeline analyzes all cWB

zero-lag and background events with a detection statisticηc > 11.3 and correlation coefficient cc > 0.7. The thresh-old on η for event follow-up is a compromise betweencomputational cost and in-depth analysis of cWB events.The BayesWave computation is performed over a 4-sec

segment of data2 centered on the event time reported bycWB. We use 1 sec of data around the event time for modelcomparison, while the remainder of the segment is used forspectral estimation. We perform the analysis in the Fourierdomain over the frequency range of 32 < f < 1024 Hzthough, for cWB candidates with central frequency fcWB <200 Hz (including GW150914), BayesWave used a maxi-mum frequency of 512 Hz to reduce the computational costof the analysis. Both the signal and the glitch model requireat least one wavelet (to make them disjoint from oneanother and the Gaussian noise model) and have amaximum of 20 wavelets allowed in the linear combina-tion. Most of the priors used in the analysis are as describedin [31] and [22], with the following changes. The prior onthe “quality factor” of the wavelets Q has been extended toinclude lower values, so that it is uniform over the interval[0.1,40]. The low Q values allow blip glitches to becorrectly characterized with a small number of wavelets.Also, the functional form of the glitch amplitude prior hasbeen modified to scale as a power law rather than anexponential in the large SNR limit. The new prior betterreflects the belief that very loud events (SNR > 100) aremore likely to be glitches than signals.Figure 4 shows the cumulative rate distribution of back-

ground events as a function of the cWBþ BayesWavedetection statistic lnBSG. The cWBþ BayesWave pipelineconsiders the triggers from all cWB search classes together(all curves in Fig. 1) as a single search. The explicit glitchmodel used by BayesWave reduces the tail in the back-ground distribution [22], so that loud background events aredown-weighted rather than grouped into different classes. In

FIG. 4. Cumulative rate distribution of background events as afunction of the cWBþ BayesWave detection statistic lnBSG. ThecWBþ BayesWave pipeline considers all cWB candidates withηc > 11.3 (combining all three curves in Fig. 1). In the equivalentof 67 400 years of data, GW150914 was the only zero-lag eventto pass all thresholds. Only one noise coincidence is rankedhigher than GW150914.

2The 4 sec segment length was shown in testing to be theminimum amount of data needed to estimate the power spectraldensity.

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the equivalent of 67 400 years of O1 data, 2374 cWB eventswarranted a BayesWave follow-up and only one noisecoincidence (lnBSG ¼ 53.1� 3.4) was ranked higher thanGW150914 (lnBSG ¼ 49.4� 0.8). GW150914 is the onlyzero-lag event to pass all thresholds. Investigations of thehighest ranking background events have revealed remark-ably similar glitches in the two detectors which, were it notfor the large, unphysical time shifts applied to the data,would be indistinguishable from a GW signal. However, thewaveform morphology of the most significant backgroundevents is in no way similar to a BBHmerger signal. Treatingall cWB candidates as coming from the same search,BayesWave estimates a FAR for GW150914 of 1 in67400 years.

IV. SEARCH SENSITIVITY

In this section, we demonstrate the ability of transientsearches to detect GWs from BBH mergers. We usesimulated gravitational waveforms that cover all threephases of BBH coalescence, i.e., inspiral, merger andringdown. The analysis is performed by adding simu-lated BBH waveforms to the detector data, and recov-ering them using the three burst pipelines described inSec. III.

A. Simulation data set

BBH systems are characterized by the masses m1 andm2, dimensionless spin vectors a1 and a2 of the twocomponent black holes, the source distance D, its

sky-location coordinates, and the inclination of the BBHorbital momentum vector relative to the line of sight toEarth. The black hole spins are obtained from the dimen-sionless spin vectors by Si ¼ m2

i ai, where jaij ≤ 1.The simulation includes binaries that are isotropically

located on the sky and isotropically oriented, with totalmasses M ¼ m1 þm2 uniformly distributed between30 and 150 M⊙, that is within a factor of ∼2 of theestimated total mass for GW150914 [29]. We generatethree separate sets, each with a fixed mass ratioq ¼ m2=m1 ∈ f0.25; 0.5; 1.0g. We assume that the blackhole spins are aligned with the binary orbital angularmomentum, with a spin magnitude uniformly distributedacross ja1;2j ∈ ½0; 0.99�. The distances are drawn fromdistributions within 3.4 Gpc such that we get goodsampling for a range of SNR values around the detectionthreshold. The simulation does not include redshift cor-rections, which introduces small systematic errors for themore distant sources. The signals are distributed uniformlyin time with a gap of 100 sec between them.The BBH waveforms analyzed in this study have been

generated using the SEOBNRv2model in the LAL softwarelibrary [42,43]. This model only accounts for the dominantl ¼ 2, m ¼ 2 GW radiated modes. The waveforms aregenerated with an initial frequency of 15 Hz. The data setsare summarized in Table I.

B. Results

To quantify the results of the study, we use the sensitiveradius which is the radius of the sphere with volumeV ¼ R

4πr2ϵðrÞdr, where ϵðrÞ is the averaged searchefficiency for sources at distance r with random skyposition and orientation [16]. For each pipeline, wecalculate the sensitive radius as a function of FAR. Theresults are shown in Fig. 5. For example, at a FAR of 1 perthousand years, the three searches show similar perfor-mance, with each detecting the simulated equal-mass BBHpopulation to a sensitive distance in the range 700 to

TABLE I. Summary of the BBH simulations used for estimat-ing search efficiency.

Total mass M ¼ m1 þm2 30–150M⊙Mass ratio, q ¼ m2=m1 0.25, 0.5, 1.0Spin magnitude ja1;2j 0–0.99Waveform model SEOBNRv2

FIG. 5. Sensitive radius for the different search pipelines for simulated BBH waveforms with different mass ratios q. The sensitiveradius measures the average distance to which the search detects with a given FAR threshold. The cWB results include all three searchclasses, with a corresponding trials factor.

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800 Mpc. To the far left side of the plots (very low FAR),the differences between pipelines are dominated by theloudest few background events; the cWB C3 search classselection for chirping events allows many BBH signals tobe recovered with very low FAR.The effect of intrinsic BBH parameters (component

masses and spins) on the sensitive radius of the threepipelines is summarized in Fig. 6. The three panels of thefigure correspond to three bins of effective spin. Effectivespin is defined as in [29]: χeff ¼ ðS1m1

þ S2m2Þ · L̂M, with L̂ the

direction of orbital angular momentum. Depending on themass and spin of the binary, the sensitive radius can varyfrom about 250 Mpc up to over 1 Gpc. Over this range,larger masses are detectable to further distances. Spinswhich are aligned with the orbital angular momentum tendto increase the sensitive radius, while antialigned spinsmake the systems more difficult to detect. For the mass/spinbin most like GW150914, 60–90 M⊙, the sensitive radiusof the searches is between 400 and 600 Mpc.

V. SOURCE CHARACTERIZATION

In [29], we present estimates for the parameters of thebinary black hole model that best describes GW150914.These parameters include the masses and spins of the

binary components, and their posterior distributions re-present our most complete description of the astrophysicalsource. In this work, we take a complementary approach,by using the outputs of the burst pipelines described inSec. III to characterize the event. Many of the burst pipelineoutputs are available in low latency, so this approach caninform follow-up studies in a timely fashion. For example,the cWB estimate of the GW150914 chirp mass wasavailable within minutes, and provided the first evidencethat this signal originated from merging black holes.Likewise, low-latency position estimates are used forcounterpart searches [28].Burst analyses are also able to estimate the time evolution

of observed waveforms, a process we refer to as waveformreconstruction. Burst waveform reconstruction algorithmsdo not rely on astrophysical models. Instead, estimates of thecoherent gravitational-wave power observed by the detectornetwork are used to reconstruct the signal. These waveformreconstructions are valuable: they provide an unbiased viewof the signal most consistent with the observatory data. Suchreconstructed signals can be used to classify the source type,compare with models, and potentially identify unexpectedfeatures. In this section, we present how the outputs of theburst pipelines were used to estimate the source position,reconstruct the waveform, and characterize the BBH source.We also compare the reconstructed waveforms with a set ofnumerical relativity waveforms, in order to check theconsistency of our results against the most precise classof models available.

A. Source localization

Three burst algorithms (cWB, BayesWave, and LIB)produce localization estimates for the GW event. These“skymaps” can be interpreted as the posterior probabilitydistribution of the source’s right ascension (α) and decli-nation (δ) given the observed data. cWB produces skymapsduring its detection process by maximizing a constrainedlikelihood on a grid over the sky; these are availablewithin minutes of the candidate’s detection. LIB andBayesWave perform more computationally expensiveanalyses, and so produce results with higher latency.LIB uses a space of single sine-Gaussian waveforms asits waveform model, and produces skymaps after 1 to 2 h,whereas BayesWave maps can take as long as several daysto be produced, since it explores a larger parameter space ofsuperpositions of sine-Gaussian waveforms. Each algo-rithm makes different and somewhat complementaryassumptions about the signal, and these assumptions affecttheir localization estimates. By localizing signals withmultiple algorithms, we can cross-check and validate thelocalization estimate and identify any systematic differencebetween the algorithms [44].An overview of the skymaps used by astronomers to

search for counterparts to GW150914 may be found in[28], including the cWB and LIB skymaps. Here, we

FIG. 6. Dependence of sensitive radius on spins of BBH. Toinvestigate the effect of spins of black holes on the detection ofBBH systems, we show the search radius R for each pipeline forvarying effective spins with mass ratio q ¼ 1 at FAR ¼10−3 1=yr. The total mass range is varied from 30–150 M⊙,while the effective spin is distributed into three bins: aligned spins(χeff ∈ ½0.33; 1�), antialigned (χeff ∈ ½−1;−0.33�) and nonspin-ning (χeff ∈ ½−0.33; 0.33�). The error bars represent the statisticaluncertainty of the sample. The cWB results include all threesearch classes, with a corresponding trials factor.

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compare cWB, LIB, and BayesWave skymaps in additionto the map produced by LALInference with binary coa-lescence templates, which samples the posterior distribu-tion of all signal parameters using signal waveforms thatcover the inspiral, merger and ringdown phase [40]. ForGW150914, we expect the LALInference map to yield arelatively precise localization, because it assumes a wave-form from a compact binary coalescence, instead of thebroad waveform classes used by the burst pipelines. Burstlocalization algorithms produce systematically larger sky-maps than template-based algorithms because they makefewer assumptions about the waveform. However, the

LALInference map reported here also includes the effectsof calibration uncertainty within the detectors, whichsignificantly widen the uncertainty of this reconstruction[45]. In principle, calibration effects could also be includedin the burst skymaps, but what is shown here represents theinformation that was available at the time electromagneticastronomy observations began [28].Figure 7 shows Mollweide projections in (α,δ) of all

skymaps considered, as well as overlays of the 50% and90% contours in a rotated frame of reference. Figure 8shows the marginal distributions for the polar angle fromthe line-of-sight between the two LIGO detectors. This

FIG. 7. All-sky projections of several skymaps produced for GW150914. Above, each map is shown by itself in celestial coordinates.Below, a rotated coordinate system shows contours defining the 50% and 90% confidence regions for four reconstructions.

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marginal distribution captures the width of the triangulationrings. All maps are consistent with some differences due tothe reconstruction algorithms. For example, the cWB maphas a “northern island” near the equator not seen in othermaps. The shape and placement of the island is affected bythe LIGO detector responses at this particular sky location[28,44]. The Hanford-Livingston network is sensitive toonly one polarization through most of the sky, and cWBuses this to constrain the reconstructed signal, with theexception of regions like the island where the networksensitivity is comparable for both polarizations. In thiscase, cWB relaxes the constraint and cannot break adegeneracy between sky locations near the island. We notethis occurs only when the triangulation ring falls near oneof these regions and may not be present for other events.To measure the similarity between the skymaps, Table II

presents the fidelity Fðp; qÞ ¼ Pi

ffiffiffiffiffiffiffiffiffipiqi

p ∈ ½0; 1� for thevarious algorithms considered, where pi and qi are theprobability densities assigned to pixels at the same coor-dinates in two different skymaps. F is closer to one if themaps are more similar and F closer to zero if the maps aredissimilar. For comparison, we also include a skymapproduced by LALInference that does not include calibra-tion uncertainties. This similarity measurement is between28% and 87% for different pairs of skymaps. To check the

robustness of the parameter estimation results, we simu-lated 29 transients with waveforms similar to GW150914,generated using the SEOBNRv2 approximant [42,43], byactuating on the mirrors at the end of the 4 km LIGO arms.We repeat the analysis on each of these hardware injections.We find similar fidelity measurements as with theGW150914 event, suggesting that this level of agreementbetween the algorithms is typical for BBHwaveforms at theSNR of GW150914.

B. Waveform reconstruction

To extract the astrophysical signal from detector noise,we reconstruct waveforms whose projection onto boththe H1 and L1 detectors is consistent with the data. ThecWB algorithm [35] performs waveform reconstructionusing a constrained maximum likelihood approach (seeSec. III A 1). BayesWave [31,41] uses a variable dimensioncontinuous wavelet basis to produce a posterior distributionfor the gravitational waveform present in a data set. Incontrast to analyses based on compact object mergertemplates, which attempt to find the best fit parameterswithin a well-defined waveform family, the cWB andBayesWave waveform reconstruction algorithms make veryweak assumptions about the form of the signal. The oLIBpipeline assumes a sine-Gaussian waveform, and so providesa less detailed reconstruction. The BayesWave version usedin this analysis assumes that the signal is ellipticallypolarized, but is otherwise free to reconstruct any astro-physical signal in the searched time-frequency volume.Figure 9 shows both the cWB point estimate and the

BayesWave 90% credible interval for the reconstructed,whitened, time-domain signal waveform, as projected ontoeach detector. The waveforms are seen to largely agree, andinclude the main expected features from a chirp signal due

FIG. 8. Marginal distributions of the polar angle defined bytriangulation. These give a measure of the width of each ring.

TABLE II. Confidence regions and fidelity values fromGW150914. The fidelity measures the similarity of two skymaps.The LALInference skymaps are shown both with (LALInf) andwithout (LALNoCE) calibration uncertainty included. Theshown burst skymaps do not include calibration uncertainties,which would make the uncertainty regions larger.

Confidence regions Fidelity50% 90% LIB BW LALInf LALNoCE

cWB 98 deg2 308 deg2 0.55 0.55 0.51 0.50LIB 208 deg2 746 deg2 � � � 0.45 0.68 0.28BW 101 deg2 634 deg2 � � � � � � 0.68 0.87LALInf 150 deg2 610 deg2 � � � � � � � � � 0.81LALNoCE 48 deg2 150 deg2 � � � � � � � � � � � �

FIG. 9. The cWB point estimate for the waveform and the 90%credible interval from the BayesWave analysis. The reconstructedwaveforms and shown data are whitened using estimated noisecurves for each detector at the time of the event. On the y-axis,sigma is a measure of the amplitude in terms of the number ofnoise standard deviations.

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to a compact object merger. The BayesWave waveformshave a median match of 94% with the posterior samplesfrom a Bayesian analysis that uses waveform templates thataccount for the inspiral, merger and ringdown phases of theBBH coalescence [40].To measure the accuracy of these reconstructions, we use

the set of simulated BBH systems described in Sec. IV. Foreach event recovered by BayesWave, we calculate thematch between the injected and reconstructed waveforms.The results are shown in Fig. 10. At fixed SNR the matchbetween the simulated and the reconstructed waveform issystematically higher for higher mass signals becauselarger mass BBH signals have a smaller time-frequencyvolume, allowing them to be fit with a smaller number ofwavelets. For the simulations similar to GW150914, in themass bin from 60 to 100 M⊙ and around network SNR 20,we see most matches are between 90% and 95% accurate.

C. Parameter estimation with genericsignal features

The source parameters of GW150914, such as compo-nent masses and spins, can be well characterized by usingan analytical model of BBH signals to compute theirposterior distributions [29]. Here, we take a differentapproach, which uses the outputs of the burst pipelinesto provide a coarse estimate of the model parameters. TheBayesWave and cWB waveform reconstructions can beused to compute a variety of parameters that summarize thesignal, such as the central frequency, duration and band-width. These parameters can then be used to help identifycharacteristics of the astrophysical system that generatedthe signal. Using waveform templates for a BBH merger,we can derive predictions for the central frequency andbandwidth of the signal in each detector as a function of themass, mass ratio and spins. Figure 11 shows the posteriordistribution for the central frequency and bandwidthderived from the BayesWave analysis of GW150914,

with an overlaid grid showing the values predicted froma black hole merger model with zero spins and total massMand mass ratio q as indicated. From our companion paper,[29], the best description of this signal yields a detectorframe total mass of M ¼ 71þ5

−4 M⊙ and a mass ratio ofq ¼ 0.82þ0.17

−0.20 . Comparing these best fit values to theregions of high posterior density shown in Fig. 11, wefind that the values lie within the 90% credible intervalproduced using the BayesWave outputs.Applying the same procedure to the 29 GW150914-like

hardware injections we found that the central frequency andbandwidth of the injected signals fell within the 50%credible interval 50% of the time, and within the 90%credible interval 89% of the time, showing that the analysisis consistent.

D. Chirp mass from time-frequency signature

The cWB pipeline obtains the time-frequency patterns ofthe events by using a discrete wavelet transform. Given apattern with N time-frequency components ðti; fiÞ,i ¼ 1;…; N from a coalescing binary, at the leadingpost-Newtonian order it is described by the time-frequencyevolution [36]

96

5π8=3

�GMc3

�5=3

tþ 3

8f−8=3 þ C ¼ 0; ð1Þ

whereM is the chirp mass parameter, G is the gravitationalconstant, c is the speed of light andC is a constant related tothe merger time. By fitting this time-frequency evolution tothe data ðti; fiÞ, we can find the mass parameter M [46].For a signal from a coalescing binary with componentmasses m1 and m2 it corresponds to the chirp mass of the

FIG. 10. Match between the whitened injected and BayesWavereconstructed waveforms for the simulation set described inSec. IV. The line indicates the median match and the shadedregion shows the 1σ uncertainty.M indicates the total mass of theblack hole binary, measured in solar masses.

FIG. 11. The posterior distributions for the central frequencyand bandwidth inferred from the whitened waveform posteriorsproduced by BayesWave for GW150914 are compared to thevalues predicted by the BBH merger templates with zero spin andtotal mass M (in units of solar mass) and mass ratio q, asindicated by the mesh of lines. The regions of high posteriorprobability are consistent with the best fit values of total mass andmass ratio [29].

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system M ¼ ðm1m2Þ3=5=ðm1 þm2Þ1=5. The chirp masserror is estimated using a bootstrapping procedure, wheremultiple subsets of data points ðti; fiÞ, i ¼ 1;…; N arerandomly selected to estimate the chirp mass.The real-time search that first detected GW150914

estimated its detector frame chirp mass to be27.6� 2.0M⊙. This result is consistent with theLALInference estimate of 30þ2

−2 M⊙ [29]. To check theaccuracy of the real-time method, we studied 29 hardwareinjections with parameters similar to those inferred forGW150914. We found that this method was able toaccurately reconstruct the chirp masses of these simulatedsignals, with a precision similar to the quoted uncertainty.

E. Overlap between reconstructed waveformand BBH model

This section presents the comparison of the recon-structed signal of the event, from BayesWave and cWB,with predictions from NR. The goal is to provide aquantitative check that the recovered signal power isconsistent with a BBH source as predicted by numericalrelativity simulations; more stringent tests of generalrelativity are available in [47]. By making very weakassumptions about the signal, the waveform reconstructionprovides a largely model-agnostic representation of the fullastrophysical signal content. In turn, the NR waveform isthe direct solution to the full Einstein equations without anyassumptions other than those necessary to numericallysolve the equations, e.g. finite discretization and finiteextraction radius. The NR waveforms used in this studywere generated by the code in [48]. The errors in the phaseand amplitude of the waveform that arise from theseapproximations are addressed in [49]. Comparing directlyto NR waveforms allows us to explore regions of parameterspace where the analytic templates [29] have not yet beentuned, such as highly precessing spin configurations andtheir higher harmonics. The study is a simple way tocompare the reconstructed astrophysical signal with thepredictions of general relativity with minimal assumptions.By comparing the NR waveforms, which cover regions ofthe parameter space which are not necessarily well modeledand include higher harmonics, with the model-independentreconstructed waveforms which can recover the full astro-physical signal content, we are sensitive to departures fromboth the analytic templates used elsewhere and from thepredictions of general relativity. In fact, we find excellentagreement between this study and the parameter estimationperformed with analytic templates, as well as with theparameter estimation procedure using only NR waveformswhich is reported in [50]. We discuss these findings below.The natural figure of merit for this comparison is the

fitting factor. We define the network match between the

reconstructed waveform sðdÞrec in detector d and the NRwaveform hNR as [51]

N ¼P

d maxt0;ϕ0ðsdrecjhNRÞd

½PdðhNRjhNRÞd�1=2 × ½PdðsdrecjsdrecÞd�1=2: ð2Þ

where the sums run over the H1 and L1 detectors andðajbÞd defines the noise-weighted inner product betweenwaveforms a and b for detector d. The fitting factor is thenetwork match N maximized over the total mass andorbital inclination [52].The reconstructed waveforms are compared to 102 BBH

waveforms that have been used previously to investigatethe feasibility of detecting precession and higher ordermodes [48,53–61]. We also include an additional four newsimulations with intrinsic parameters motivated by param-eter estimation studies of GW150914 [29]. Note that theNR simulations are not a continuous representation of theparameter space, but rather a discrete set of astrophysicallyinteresting, generic systems. Each NR waveform, hNR, isparametrized by the mass ratio q ¼ m2=m1 < 1 and spinconfiguration of the system.Figure 12 shows the fitting factors between BayesWave

and cWB and the NR waveforms in terms of the massratio q and the dot products between the componentspins and the orbital angular momentum, ai · L̂ fori ¼ 1, 2. The figure also serves to demonstrate the coverageof the parameter space by the NR simulations. We find thatthe parameter space of NR waveforms favored by bothalgorithms is similar. Specifically, nearly symmetric massconfigurations and small values for ai · L̂ for both compo-nents are preferred, although the lack of variation in the

FIG. 12. Fitting factors between cWB (left) and BayesWave(right) and the NR waveforms, in terms of the mass ratio q and thedot products between the component spins and the orbital angularmomentum, a1 · L̂; a2 · L̂. The quoted BayesWave fitting factorvalues are the median values evaluated across 1000 posteriorwaveform samples.

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fitting factor across the spin space suggests this is notstrongly constrained.The BayesWave and cWB reconstructed waveforms

have a fitting factor with the best fit NR waveform of0.95 and 0.87, respectively. Fits within 1% of the best fitvalue are achieved with detector frame total mass in therange 66.4–74.8 M⊙ for BayesWave and 67.9–75.7 M⊙for cWB. This is in excellent agreement with the range66–75 M⊙ estimated using LALInference [29]. The chirpmass of NR waveforms within 1% of the best fit to theBayesWave and cWB reconstructions is in the range27.4–32.6 M⊙ and 27.8–33.0 M⊙, again with close over-lap to the LALInference result of 29–33 M⊙.In addition to matching parameter estimation performed

using analytic waveform models in [29], the parameterbounds shown here are consistent with those obtained viathe time-frequency analyses in Secs. V C and VD.Findings similar to those here are reported in [50] wherea suite of NR waveforms, including those used in this study,are compared directly with the data in a novel Bayesiananalysis. Again, the parameter space preferred by that studyclearly overlaps with that here. The agreement between theanalytic waveform results and the Bayesian NR analysishelps to validate the use of those waveform templates.Meanwhile, the overlap with the model-independent recon-structions here demonstrates that there is no significantadditional signal content which the NR waveforms fail torepresent, as would be the case for sources other than BBH.The concordance among the findings from these threestudies further serves to highlight the BBH origin ofGW150914.

VI. DISCUSSION

All-sky searches for short-duration gravitational-wave bursts scan a broad parameter space to identify thepresence of gravitational-wave signals in the data. Theydiscovered GW150914 in a low-latency online analysis,and identified it as clearly distinct from detector noiseevents. Further analysis of GW150914 showed that thereconstructed waveform of the signal is consistent withexpectations for a binary black hole merger. Outputs of theburst pipelines were also used to estimate the massparameters of the source, in agreement with more special-ized techniques.The discovery of GW150914 is a turning point in

gravitational-wave astronomy. At the time of the discovery,low-latency burst searches were configured to search abroad parameter space, similar to gravitational-wave burstsearches performed during the initial detector era. The largesearch parameter space was seen to overlap with high-massbinary black hole signals in studies with simulated data, anobservation confirmed by the detection of GW150914.Looking towards the future, the emphasis on searches withminimal assumptions of the waveform morphology allowsfor gravitational-wave burst searches to explore the vast

discovery space of gravitational-wave transients from avariety of potential sources.Beyond the challenge of detecting gravitational waves,

burst parameter estimation tools, which make weak signalassumptions, have demonstrated their ability to extractastrophysical information about the progenitor ofGW150914. Rapid sky localization of transient sourceswill facilitate multimessenger astronomy and allow forimproved characterization of gravitational-wave signalprogenitors. Many of the tools used for GW150914, suchas waveform reconstruction, have applications beyondgravitational waves from binary coalescences.The methods described in this work will also be used to

search the full data set from the first observing run in theadvanced detector era and beyond. Gravitational-waveburst searches have shown, through their detection andanalysis of GW150914, that they are ready to contribute toan era of gravitational-wave astronomy.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the support of theUnited States National Science Foundation (NSF) for theconstruction and operation of the LIGO Laboratory andAdvanced LIGO as well as the Science and TechnologyFacilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of AdvancedLIGO and construction and operation of the GEO 600detector. Additional support for Advanced LIGO was pro-vided by the Australian Research Council. The authorsgratefully acknowledge the Italian Istituto Nazionale diFisica Nucleare (INFN), the French Centre National de laRecherche Scientifique (CNRS) and the Foundation forFundamental Research on Matter supported by theNetherlands Organisation for Scientific Research, forthe construction and operation of the Virgo detector andthe creation and support of the EGO consortium. The authorsalso gratefully acknowledge research support from theseagencies as well as by the Council of Scientific andIndustrial Research of India, Department of Science andTechnology, India; Science & Engineering Research Board(SERB), India; Ministry of Human Resource Development,India; the SpanishMinisterio de Economía yCompetitividad;the Conselleria d’Economia i Competitivitat and Conselleriad’Educació; Cultura i Universitats of the Govern de les IllesBalears; theNational Science Centre of Poland; the EuropeanCommission; the Royal Society; the Scottish FundingCouncil; the Scottish Universities Physics Alliance; theHungarian Scientific Research Fund (OTKA); the LyonInstitute of Origins (LIO); the National ResearchFoundation of Korea; Industry Canada and the Province ofOntario through the Ministry of Economic Development andInnovation; the National Science and Engineering ResearchCouncil Canada; Canadian Institute for Advanced Research;the Brazilian Ministry of Science, Technology, and

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Innovation; Russian Foundation for Basic Research; theLeverhulme Trust; the Research Corporation; Ministry ofScience and Technology (MOST), Taiwan; and the KavliFoundation. The authors gratefully acknowledge the support

of the NSF, STFC, MPS, INFN, CNRS and the State ofNiedersachsen/Germany for provision of computationalresources. This article has been assigned the documentnumber LIGO-P1500229.

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S. Walsh,16,8,29 G. Wang,12 H. Wang,44 M. Wang,44 X. Wang,70 Y. Wang,50 R. L. Ward,20 J. Warner,37 M. Was,7 B. Weaver,37

L.-W. Wei,52 M. Weinert,8 A. J. Weinstein,1 R. Weiss,10 T. Welborn,6 L. Wen,50 P. Weßels,8 T. Westphal,8 K. Wette,8

J. T. Whelan,112,8 D. J. White,86 B. F. Whiting,5 D. Williams,36 R. D. Williams,1 A. R. Williamson,91 J. L. Willis,133

B. Willke,17,8 M. H. Wimmer,8,17 W. Winkler,8 C. C. Wipf,1 H. Wittel,8,17 G. Woan,36 J. Worden,37 J. L. Wright,36 G. Wu,6

J. Yablon,82 W. Yam,10 H. Yamamoto,1 C. C. Yancey,62 M. J. Yap,20 H. Yu,10 M. Yvert,7 A. Zadrożny,110 L. Zangrando,42

M. Zanolin,97 J.-P. Zendri,42 M. Zevin,82 F. Zhang,10 L. Zhang,1 M. Zhang,119 Y. Zhang,112 C. Zhao,50 M. Zhou,82 Z. Zhou,82

X. J. Zhu,50 M. E. Zucker,1,10 S. E. Zuraw,101 and J. Zweizig1

(LIGO Scientific Collaboration and Virgo Collaboration)

1LIGO, California Institute of Technology, Pasadena, California 91125, USA2Louisiana State University, Baton Rouge, Louisiana 70803, USA

3Università di Salerno, Fisciano, I-84084 Salerno, Italy4INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy

5University of Florida, Gainesville, Florida 32611, USA6LIGO Livingston Observatory, Livingston, Louisiana 70754, USA

7Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc,CNRS/IN2P3, F-74941 Annecy-le-Vieux, France

8Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany9Nikhef, Science Park, 1098 XG Amsterdam, Netherlands

10LIGO, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA11Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil

12INFN, Gran Sasso Science Institute, I-67100 L’Aquila, Italy13INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy

14Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India15International Centre for Theoretical Sciences, Tata Institute of Fundamental Research,

Bangalore 560012, India16University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA

17Leibniz Universität Hannover, D-30167 Hannover, Germany18Università di Pisa, I-56127 Pisa, Italy

19INFN, Sezione di Pisa, I-56127 Pisa, Italy20Australian National University, Canberra, Australian Capital Territory 0200, Australia

21The University of Mississippi, University, Mississippi 38677, USA22California State University Fullerton, Fullerton, California 92831, USA

23LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, 91400 Orsay, France24Chennai Mathematical Institute, Chennai 603103, India25Università di Roma Tor Vergata, I-00133 Roma, Italy

26University of Southampton, Southampton SO17 1BJ, United Kingdom27Universität Hamburg, D-22761 Hamburg, Germany

28INFN, Sezione di Roma, I-00185 Roma, Italy29Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm, Germany

30APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu,Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France

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31Montana State University, Bozeman, Montana 59717, USA32Università di Perugia, I-06123 Perugia, Italy

33INFN, Sezione di Perugia, I-06123 Perugia, Italy34European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy

35Syracuse University, Syracuse, New York 13244, USA36SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom

37LIGO Hanford Observatory, Richland, Washington 99352, USA38Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary

39Columbia University, New York, New York 10027, USA40Stanford University, Stanford, California 94305, USA

41Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy42INFN, Sezione di Padova, I-35131 Padova, Italy

43CAMK-PAN, 00-716 Warsaw, Poland44University of Birmingham, Birmingham B15 2TT, United Kingdom

45Università degli Studi di Genova, I-16146 Genova, Italy46INFN, Sezione di Genova, I-16146 Genova, Italy

47RRCAT, Indore, MP 452013, India48Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia

49SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom50University of Western Australia, Crawley, Western Australia 6009, Australia

51Department of Astrophysics/IMAPP, Radboud University Nijmegen,6500 GL Nijmegen, Netherlands

52Artemis, Université Côte d’Azur, CNRS, Observatoire Côte d’Azur,CS 34229 Nice cedex 4, France

53MTA Eötvös University, “Lendulet” Astrophysics Research Group, Budapest 1117, Hungary54Institut de Physique de Rennes, CNRS, Université de Rennes 1,

F-35042 Rennes, France55Washington State University, Pullman, Washington 99164, USA

56Università degli Studi di Urbino “Carlo Bo,” I-61029 Urbino, Italy57INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy

58University of Oregon, Eugene, Oregon 97403, USA59Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University,

Collège de France, F-75005 Paris, France60Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland

61VU University Amsterdam, 1081 HV Amsterdam, Netherlands62University of Maryland, College Park, Maryland 20742, USA

63Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology,Atlanta, Georgia 30332, USA

64Institut Lumière Matière, Université de Lyon, Université Claude Bernard Lyon 1,UMR CNRS 5306, 69622 Villeurbanne, France

65Laboratoire des Matériaux Avancés (LMA), IN2P3/CNRS, Université de Lyon,F-69622 Villeurbanne, Lyon, France

66Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain67Università di Napoli “Federico II,” Complesso Universitario di Monte S. Angelo,

I-80126 Napoli, Italy68NASA/Goddard Space Flight Center, Greenbelt, Maryland 20771, USA69Canadian Institute for Theoretical Astrophysics, University of Toronto,

Toronto, Ontario M5S 3H8, Canada70Tsinghua University, Beijing 100084, China

71Texas Tech University, Lubbock, Texas 79409, USA72The Pennsylvania State University, University Park, Pennsylvania 16802, USA

73National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China74Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia

75University of Chicago, Chicago, Illinois 60637, USA76Caltech CaRT, Pasadena, California 91125, USA

77Korea Institute of Science and Technology Information, Daejeon 305-806, Korea78Carleton College, Northfield, Minnesota 55057, USA

79Università di Roma “La Sapienza,” I-00185 Roma, Italy80University of Brussels, Brussels 1050, Belgium

81Sonoma State University, Rohnert Park, California 94928, USA

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82Northwestern University, Evanston, Illinois 60208, USA83University of Minnesota, Minneapolis, Minnesota 55455, USA

84The University of Melbourne, Parkville, Victoria 3010, Australia85The University of Texas Rio Grande Valley, Brownsville, Texas 78520, USA

86The University of Sheffield, Sheffield S10 2TN, United Kingdom87University of Sannio at Benevento, I-82100 Benevento, Italy

and INFN, Sezione di Napoli, I-80100 Napoli, Italy88Montclair State University, Montclair, New Jersey 07043, USA

89Università di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy90INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy

91Cardiff University, Cardiff CF24 3AA, United Kingdom92National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

93School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom94Indian Institute of Technology, Gandhinagar, Ahmedabad, Gujarat 382424, India

95Institute for Plasma Research, Bhat, Gandhinagar 382428, India96University of Szeged, Dóm tér 9, Szeged 6720, Hungary

97Embry-Riddle Aeronautical University, Prescott, Arizona 86301, USA98University of Michigan, Ann Arbor, Michigan 48109, USA

99Tata Institute of Fundamental Research, Mumbai 400005, India100American University, Washington, D.C. 20016, USA

101University of Massachusetts-Amherst, Amherst, Massachusetts 01003, USA102University of Adelaide, Adelaide, South Australia 5005, Australia103West Virginia University, Morgantown, West Virginia 26506, USA

104University of Biał ystok, 15-424 Białystok, Poland105SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom

106IISER-TVM, CET Campus, Trivandrum, Kerala 695016, India107Institute of Applied Physics, Nizhny Novgorod, 603950, Russia

108Pusan National University, Busan 609-735, Korea109Hanyang University, Seoul 133-791, Korea

110NCBJ, 05-400 Świerk-Otwock, Poland111IM-PAN, 00-956 Warsaw, Poland

112Rochester Institute of Technology, Rochester, New York 14623, USA113Monash University, Victoria 3800, Australia

114Seoul National University, Seoul 151-742, Korea115University of Alabama in Huntsville, Huntsville, Alabama 35899, USA

116ESPCI, CNRS, F-75005 Paris, France117Università di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy

118Southern University and A&M College, Baton Rouge, Louisiana 70813, USA119College of William and Mary, Williamsburg, Virginia 23187, USA

120Instituto de Física Teórica, University Estadual Paulista/ICTP South American Institutefor Fundamental Research, Sao Paulo, SP 01140-070, Brazil

121University of Cambridge, Cambridge CB2 1TN, United Kingdom122IISER-Kolkata, Mohanpur, West Bengal 741252, India

123Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX, United Kingdom124Whitman College, 345 Boyer Avenue, Walla Walla, Washington 99362 USA

125National Institute for Mathematical Sciences, Daejeon 305-390, Korea126Hobart and William Smith Colleges, Geneva, New York 14456, USA

127Janusz Gil Institute of Astronomy, University of Zielona Góra,65-265 Zielona Góra, Poland

128Andrews University, Berrien Springs, Michigan 49104, USA129Università di Siena, I-53100 Siena, Italy

130Trinity University, San Antonio, Texas 78212, USA131University of Washington, Seattle, Washington 98195, USA

132Kenyon College, Gambier, Ohio 43022, USA133Abilene Christian University, Abilene, Texas 79699, USA

†Deceased, May 2015.‡Deceased, March 2015.

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